BASIC PRINCIPLES OF MIXED VIRTUAL ELEMENT METHODS
BASIC PRINCIPLES OF MIXED VIRTUAL ELEMENT METHODS
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DOI：
10.1051/m2an/2013138
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发表时间：
2014-07-01
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影响因子：
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通讯作者：
Marini, L. Donatella
中科院分区：
文献类型：
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作者：
Brezzi, F.;Falk, Richard S.;Marini, L. Donatella
本文的目的是简单介绍虚拟单元法在H(Div)-协调向量场(或更一般地，(n-1)-Cochains)离散化中的推广。正如我们将看到的，这里提出的方法可以被看作是所谓的BDM族的扩展，以处理更一般的元素几何(例如具有几乎任意几何的多边形)。为了简单起见，我们将自己限制在二维情况下，目的是为了让基本哲学变得清晰。然而，我们考虑任意精度k(在有限元框架中处理任意阶多项式的虚拟单元模拟)。
The aim of this paper is to give a simple, introductory presentation of the extension of the Virtual Element Method to the discretization of H(div)-conforming vector fields (or, more generally, of (n - 1) - Cochains). As we shall see, the methods presented here can be seen as extensions of the so-called BDM family to deal with more general element geometries (such as polygons with an almost arbitrary geometry). For the sake of simplicity, we limit ourselves to the 2-dimensional case, with the aim of making the basic philosophy clear. However, we consider an arbitrary degree of accuracy k (the Virtual Element analogue of dealing with polynomials of arbitrary order in the Finite Element Framework).